Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function

Baoquan Zhou and Ningzhong Shi

Chaos, Solitons & Fractals, 2024, vol. 189, issue P2

Abstract: This paper examines a stochastic SEIS epidemic model motivated by Black–Karasinski process. First, it is shown that Black–Karasinski process is a both biologically and mathematically reasonable assumption compared with existing stochastic modeling methods. By analyzing the diffusion structure of the model and solving the relevant Kolmogorov–Fokker–Planck equation, a complete characterization for explicitly approximating the stationary density function near some quasi-positive equilibria is provided. Then for the deterministic model, the basic reproduction number and related asymptotic stability are studied. Finally, several numerical examples are given to substantiate our theoretical findings.

Keywords: Stochastic SEIS epidemic model; Probability density function; Kolmogorov–Fokker–Planck equation; Black–Karasinski process; Local stability (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p2:s0960077924012657

DOI: 10.1016/j.chaos.2024.115713

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